Multiscale topology optimization for solid–lattice–void hybrid structures through an ordered multi-phase interpolation

In this paper, we propose a new multiscale topology optimization method to design the solid–lattice–void hybrid structures. A novel ordered solid–lattice–void interpolation model has been developed that realizes smooth transition across the solid, lattice, and void phases, and very importantly, this interpolation model coordinates well between the multiple variables describing the lattice configuration and the relative density variable indicating the solid, lattice, or void status. Specifically, a multi-variable lattice resulted from topology optimization is accepted as the candidate lattice and its effective elastic properties are established through regressive fitting. Then, the ordered solid–lattice–void​ interpolation formula is developed, which unifies the multi-phase interpolation that allows exceeding the lattice upper/lower limit to reach the solid/void status for the elements. Finally, the multiscale topology optimization algorithm is formulated and implemented for solid–lattice–void hybrid structure design. Numerical examples are studied which demonstrate significant structural performance improvement compared with pure lattice-infilled structures. Finally, additive manufacturing and mechanical tests are conducted to validate the effectiveness of the proposed method.